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Measuring the compatibility of petroleum-based hydrocarbon resins in elastomers.

Hydrocarbon resins are typically defined as low molecular weight polymers with high softening points produced from various petroleum fractions. They are commonly employed in rubber formulations to improve processing, influence surface tack or otherwise modify the viscoelastic properties of the compound. In each of these cases, a degree of compatibility between the hydrocarbon resin and the other polymeric ingredients in the formulation is required.

Hamed identified the role of the hydrocarbon resin as a tackifier in rubber formulations (ref. 1). A compatible resin effectively lowers the viscosity of the blend at low shear rates, improving contact and promoting interdiffusion of the polymers at the bond surface, while also increasing the green strength of the blend. Powers investigated the compatibility of coumarone-indene resin with different structures but similar softening points in natural rubber, styrene-butadiene rubber and acrylonitrile-butadiene rubber. (ref. 2). It was found that solubility of the resins was the most important factor influencing physical properties of the blends. In addition, it was also noted that a certain level of aromatic structure in a petroleum resin was required for solubility in oil-extended styrene-butadiene rubber vulcanizates. Aubrey forwarded the use of solubility parameters in predicting the compatibility of various rosins and natural rubber, and demonstrated the utility of phase diagrams based on calculated interaction (x) parameters (ref. 3). In addition to these academic studies, a review of the patent literature provides citations of hydrocarbon resins in novel plasticizing systems for elastomers. Examples provided in the literature include replacing aromatic oils with hydrocarbon resins and non-labeled processing oils, citing improvements in the viscoelastic properties of the rubber compound (refs. 4 and 5). Kralevich et al. demonstrated the use of novel hydrocarbon resins to alter the viscoelastic properties of the tire tread compound (ref. 6). Compatibility of the components was a key performance criterion.

Hydrocarbon resins are added at high loadings as tackifying aids in thermoplastic polymers commonly used in hot melt adhesives. The hydrocarbon resin must be compatible with the polymer in order to formulate effective pressure sensitive adhesives (refs. 7 and 8). The change in viscoelastic properties of resin-elastomer blends in reference to the pure polymers was used to measure compatibility. Again, compatibility of the hydrocarbon resin with the diene block of the styrene-butadiene-styrene or styrene-isoprene-styrene triblock copolymers was central to adhesive performance. More recently, metallocene polyolefins have been introduced as polymers for use in adhesive formulations. These polymers typically require highly aliphatic or hydrogenated hydrocarbon resins for useful adhesives to be produced.

In the current study, a series of hydrocarbon resins based on C5 and C9 fractions and styrenic monomers possessing similar glass transition temperatures and molecular weights but widely varying composition are mechanically blended with a set of elastomers in order to elucidate what structural parameters lead to compatibility. The blends are melt mixed using a mechanical process. Thermal analysis and dynamic mechanical testing of the binary blends is performed to measure the glass transition temperature and viscoelastic properties. Compatibility is determined by comparing the properties of the blends to the pure polymers. Solubility parameters are calculated for the polymers and resins in order to determine if they can be used to accurately predict the degree of compatibility and validate empirical models.



Tables 1 and 2 list the polymer materials used in the study. All materials were used as received. The hydrocarbon resins represent a range of C5, C9 and styrenic monomer compositions and will be described in subsequent sections. The composition of the ethylene-propylene-diene rubber (EPDM) is 55 weight percent ethylene monomer. A high cis (96%) polybutadiene rubber (BR) grade was used. The natural rubber (NR) is a constant viscosity (60 Mooney) grade. The emulsion styrene butadiene rubber (ESBR) contains 23.5 weight percent styrene monomer and low vinyl content (13%); the solution styrene butadiene rubber (SSBR) contains 25 weight percent styrene monomer and high vinyl content (45%). Nitrile rubber (NBR) containing 33 weight percent acrylonitrile monomer was used. The aliphatic/aromatic proton ratios (nuclear magnetic resonance) and [T.sub.g]s of the hydrocarbon resins are provided in table 3. The [T.sub.g] data of the neat elastomers are given in table 4.

Blend processing

Binary hydrocarbon resin/elastomer blends were combined in a lab-scale Banbury internal mixer for four minutes at a starting point of 100[degrees]C at 60 rpm. Internal blend temperature rose to approximately 120[degrees]C during mixing, well above the softening points of the hydrocarbon resins. Blends were removed and allowed to cool overnight prior to analysis.

Thermal and mechanical testing

Thermal analysis was conducted using differential scanning calorimetry (DSC) at a heating rate of 20[degrees]C per minute during a single heating cycle. Glass transition ([T.sub.g]) inflection point was recorded. Dynamic mechanical analysis (DMA) was performed on a parallel plate rheometer using 8 mm plates and a 1.5 mm gap. Loss tangent (tan 15) was recorded over a temperature range sufficient to capture transitions throughout the viscoelastic spectrum.

[T.sub.g] of the binary blend ([]) was calculated by the Fox equation for amorphous polymers without strong interactions (ref. 9):

1/[] = [w.sub.1]/[T.sub.g1] + [w.sub.2]/[T.sub.g2] (1)

where [w.sub.i] represents the weight fraction of component i in the blend and [] represents the [T.sub.g] of the pure component i. The result from equation 1 represents the ideal case of assuming complete miscibility. Miscible polymers interact at the segmental scale and exhibit properties of a single phase material. A compatible polymer blend does not assume a single phase, but implies a high level of interaction between phases and the exhibition of uniform physical properties (ref. 10).

Solubility parameters

Solubility parameters ([[delta].sub.p]) were calculated by summation of tabulated molar attraction constants (G) according to the relationship

[[delta].sub.p] = (d[SIGMA]G)/m (2)

where d is the density of the polymer and m the molecular weight flee 11). The basis for hydrocarbon resin solubility parameter calculations was an inventory of the monomer components of the feedstock fractions. It is acknowledged that the final structure of the monomer as incorporated in the resin may not be adequately represented using this approximation. For example, it is believed a high degree of cyclization can occur during the cationic polymerization of diene, cyclic and mono olefin monomers. Pearson correlation coefficients (r) were calculated based on the following equation

[r.sub.xy] = [SIGMA](x-[??])(y-[??])/[([SIGMA][(x-[??]).sup.2] [SIGMA][(y-[??]).sup.2]).sup.1/2] (3)

where [??] and [??], are the sample means of x and y.

Results and discussion

There are several techniques employed to process polymer blends. A typical method involves using a common solvent. If the polymers have different refractive indexes, the solution can be simply observed for relative clarity or haziness, providing a qualitative measure of compatibility. Further, the polymer blend can be cast from solution to provide samples for characterization. In each case, it is important to consider the solvent choice, as dissimilar solvent-polymer interactions may result in inaccurate results. In addition, casting conditions can also affect observed results (ref. 12). Most commercial literature that catalogues hydrocarbon resin/polymer solubility is reported based on observations of solution behavior. However, few commercial uses of resin/elastomer blends are processed from solvent. A standard technique is melt mixing, typically in an internal-style mixer common to the rubber industry or the sigma-style mixers associated with adhesive formulating. For blends of partial compatibility, the processing method can influence the results so it is imperative to mix the polymers in a manner representative of the final application when evaluating blend behavior in a laboratory setting. To best reproduce actual conditions, mechanical mixing was employed for the blends evaluated in the current study.

Both thermal and mechanical techniques are employed to evaluate solid-state polymer blends. For polymers having widely separated [T.sub.g]S, DSC can be used to quantify the compatibility of resulting blends. If the perfectly miscible case is assumed, the resulting blend [T.sub.g] can be calculated according to equation 1. The ideal case can be used as a comparative data point from which to assess the compatibility of the blends based on experimental results. The degree of deviation from the calculated [T.sub.g] can be used to determine the extent of compatibility when one component of the blend may have a weak response. Disregarding any compositional variability within each polymer studied, blends exhibiting incompatibility will exhibit a broadening in the [T.sub.g] of the majority component, the strength of which is determined by the degree of compatibility.

Thermal and mechanical analysis

In the present study, the degree of compatibility between the majority component (elastomer, 80% by weight) and minority component (hydrocarbon resin, 20% by weight) is determined by measuring the shift in the [T.sub.g] of the blend compared to the Tg of the pure elastomer ([DELTA][T.sub.g]). Differential scanning calorimetry can be used to probe the phase behavior in blends of amorphous polymers. The hydrocarbon resins exhibit a strong transition when measured as a pure component by DSC, but did not resolve separate, individual transitions in any of the blended samples. As an illustrative example, figure 1 compares DSC curve data highlighting the shift in [T.sub.g] for the blend series based on ESBR. A qualitative measure of the degree of compatibility is shown in the change of position and breadth of the transition.

Dynamic mechanical analysis can be used to provide high resolution data regarding polymer transitions. DMA results can be more sensitive than DSC to small concentrations of a second polymer phase, or motions associated with smaller segments of the polymer chain (ref. 12). Again, the impact on the position and breadth of the component transitions are used to quantify the compatibility of the blends. Compatible blends will produce a relatively sharp single tan [delta] peak at a temperature between the two pure component [T.sub.g]S. Incompatibility or partial compatibility (microheterogeneity) will result in a broadening of the transition and a peak shift away from the original position of the majority component. An illustrative example of the DMA data is provided in figure 2, comparing the change in peak tan 8 of the ESBR elastomer as a function of hydrocarbon resin addition. In general, the peak position, height and breadth can provide a qualitative measure of polymer-resin interaction.

Tabulated results for DSC measurements are provided in appendix 1. Blend [T.sub.g]S for the ideal case of complete miscibility, as calculated using equation 1, are also provided for reference. Tabulated results for DMA measurements are provided in appendix 2. The results from DSC and DMA measurements are provided together in figures 3-8, as the [DELTA][T.sub.g]s are compared for each elastomer as a function of hydrocarbon resin in the blend. Consistent with the method of analysis outlined above, the higher the [DELTA][T.sub.g] value, the greater the degree of compatibility.

EPDM/resin blends show higher [DELTA][T.sub.g] values for the C5-based aliphatic resins, and the values decrease with increasing aromatic composition in the resin, with aMS showing little to no [T.sub.g] shift (figure 3). Overall, there is good qualitative agreement between thermal and mechanical analysis tools. In general for the NR and BR blends (figures 4 and 5, respectively), a clear trend is less apparent, with most resins showing moderate [DELTA][T.sub.g] shifts. DSC and DMA results are not well correlated. For the two SBR grades, [DELTA][T.sub.g] values increase with increasing aromatic composition of the resin component. The SBRs evaluated in the study (figures 6 and 7) both show large [T.sub.g] shifts with C9-based aromatic resins and the styrenic resin, with moderate [DELTA][T.sub.g] values for the more aliphatic resins. DSC and DMA data varies in magnitude but trends similarly for the SBR/resin blends. For NBR (figure 8), again [DELTA][T.sub.g] values increase with resin aromaticity. There is a much stronger overall [DELTA][T.sub.g] response for the DSC measurements compared to DMA, which is inconsistent with the other elastomer measurements.

An interpretation of the results considers the relative polarity of the elastomers and hydrocarbon resins. The elastomers can be ranked, in terms of polarity: EPDM < NR, BR < ESBR, SSBR < NBR. The hydrocarbon res ins are typically ranked according to their aliphatic/aromatic content. Considering the spectrum of compositions, there exists a basis for rationalizing the compatibility data set. EPDM, the least polar elastomer, shows higher [DELTA][T.sub.g] shifts for the more aliphatic C5 resins, with a decrease in shift with increasing aromatic content. NBR is the most polar elastomer and exhibits the opposite trend. These data suggest that resins with higher aromatic content are more compatible with elastomers containing monomers with higher polarity. The data from the two SBR grades support the argument, showing higher [T.sub.g] shifts with more aromatic resin content. The rationale used above for comparing the data based on elastomer and resin polarity does not appear to be consistent for the NR and BR blends. No clear trends based on polarity are evident in the case of NR and BR blends.

The phenomenon of partial compatibility was investigated further by comparing the DMA [T.sub.g] shifts as a function of hydrocarbon resin loading. For partially compatible systems, properties will reach a limiting value as a function of loading of the minor component. Focusing on ESBR as the elastomer (figure 6), the ESBR/C5-I blend produced the lowest [DELTA][T.sub.g], while the ESBR/aMS blend produced the largest shift. These results indicate that the compatibility of aMS resin is higher than C5-I. Both resins were further blended with ESBR at the following weight ratios (ESBR/resin): 90/10, 80/20, 70/30 and 60/40. Figures 9 and 10 provide [DELTA][T.sub.g] as a function of increasing resin loading for C5-I and aMS resins, respectively. The [DELTA][T.sub.g] data of C5-I display a maximum value at 80/20 loading, and remain unchanged at the higher resin loadings. In contrast, the [DELTA][T.sub.g] for the aMS resin increases linearly with resin loading with a much higher absolute shift value. In both figures, [DELTA][T.sub.g]S based on calculations using equation 1 are provided for reference. By comparison, the data suggest the C5-I resin reaches a compatibility limit at approximately 20 weight percent loading, while the aMS resin is fully compatible across the entire loading range.

Solubility, parameter analysis

There is agreement that a solubility parameter approach can help predict phase behavior of non-polar amorphous polymer pairs that have no specific interactions driving miscibility. The approach was previously validated for binary polymer systems by Krause, noting that solubility parameters calculated from group molar attraction constants could accurately predict miscibility (ref. 13). Coleman et al. provide a guideline for predicting miscibility based on specific polymer-polymer interactions (ref. 14). In the absence of strong polymer-polymer interactions and only relying on weak forces to drive miscibility, the difference in solubility parameters [([DELTA][[delta].sub.p.sup.2]).sup.1/2] needs to be less than 0.1 (dispersive forces only) to 1.0 (polar forces) to achieve miscibility. The window for miscibility is wider as polymer molecular weight is decreased, with miscibility predicted for [([DELTA][[delta].sub.p.sup.2]).sup.l/2] as high as 0.35 for polymers with degrees of polymerization less than 100 (ref. 13).

The solubility parameters of the elastomers and hydrocarbon resins utilized in this study were calculated according to equation 2 and are provided in table 5. The cationic polymerization of C5 streams can lead to mixed structures, including cyclization. It has been suggested that the piperylene monomer is particularly prone to dimerization by addition to a cycloaliphatic monomer prior to polymerization (ref. 15). Internal cyclization is also thought to occur during the acid-catalyzed polymerization of linear C5 diolefins (ref. 2). The calculated solubility parameters are based on a cycloaliphatic structure polymerized through the exocyclic double bond, shown in figure 11. Values for solubility parameter differences [([DELTA][[delta].sub.p.sup.2]).sup.1/2] for the binary blends are given in table 6. Basing calculations on the cycloaliphatic piperylene dimer as a monomer, there was much higher agreement between [([DELTA][[delta].sub.p.sup.2]).sup.1/2] values and experimental results. The result is especially true for the C5 resins 1 and II, which are largely based on piperylene.

It is apparent that for these low molecular weight resins, several blends fall near or below 0.35 [([DELTA][[delta].sub.p.sup.2]).sup.1/2] value, indicating compatibility or even miscibility. The shift in [T.sub.g] of the elastomer-resin blends compared to the original elastomer [T.sub.g] can be compared to [([DELTA][[delta].sub.p.sup.2]).sup.1/2] values to determine the predictive power of the solubility parameter approach. Table 6 also provides Pearson correlation coefficients based on a comparison between [([DELTA][[delta].sub.p.sup.2]).sup.1/2] and DMA [DELTA][T.sub.g] data. Inverse predictive relationships were found for NBR, ESBR, NR and EPDM blends, while weak or no relationship was recorded for SSBR or BR blends. The [([DELTA][[delta].sub.p.sup.2]).sup.1/2] values for the NBR blends are much higher than the other elastomer systems, reflecting the comparably low [DELTA][T.sub.g] experimental values. Finally, figure 12 presents DMA [DELTA][T.sub.g] data versus [([DELTA][[delta].sub.p.sup.2]).sup.1/2] for NR, ESBR and NBR blends. The trend indicates that for blends with high correlation coefficients, there is a strong inverse relationship between a measurement of compatibility and calculated solubility parameter differences.

Summary and conclusions

Many applications require a degree of compatibility when employing blends of hydrocarbon resins and elastomers. It has been shown that the degree of compatibility can be quantified by comparing the magnitude of shift in both thermal and mechanical measurements of the [T.sub.g] of binary blends. In general, hydrocarbon resins with higher aliphatic composition (C5 fraction) produced a higher [T.sub.g] shift in elastomers with low polarity. Hydrocarbon resins with higher aromatic compositions (C9 fraction or styrenic) produced higher shifts in the [T.sub.g] of higher polarity elastomers. Comparing calculated solubility parameters can be an effective means to predict the extent of compatibility for certain blends of hydrocarbon resins and elastomers.

Appendix 1 - DSC results for 80/20 (wt./wt.) polymer blends

               [T.sub.g]    [T.sub.g] Shift   FOX [T.sub.g]
              ([degree]C)     ([degree]C)      ([degree]C)

EPDM              -42              -                -
EPDM/C5-I         -36              7               -27
EPDM/C5-II        -36              6               -28
EPDM/C5-C9        -39              3               -29
EPDM/C9-I         -39              3               -27
EPDM/C9-II        -40              2               -28
EPDM/aMS          -40              2               -27
NR                -59              -                -
NR/C5-I           -57              2               -43
NR/C5-II          -55              4               -43
NR/C5-C9          -55              4               -44
NR/C9-I           -55              4               -43
NR/C9-II          -54              5               -43
NR/aMS            -54              5               -43
BR               -103              -                -
BR/C5-I          -102              1               -85
BR/C5-II          -99              4               -85
BR/C5-C9          -92             11               -86
BR/C9-I           -98              5               -85
BR/C9-II          -99              4               -85
BR/aMS            -97              6               -85

               [T.sub.g]    [T.sub.g] Shift   FOX [T.sub.g]
              ([degree]C)     ([degree]C)      ([degree]C)

ESBR              -50
ESBR/C5-I         -47              3               -34
ESBR/C5-II        -43              7               -35
ESBR/C5-C9        -42              8               -36
ESBR/C9-I         -42              8               -34
ESBR/C9-II        -42              8               -35
ESBR/aMS          -41              9               -34
SSBR              -9               _                -
SSBR/C5-I         -4               4                2
SSBR/C5-II        -3               5                2
SSBR/C5-C9        -4               5                1
SSBR/C9-I         -2               7                3
SSBR/C9-II        -2               7                2
SSBR/aMS           0               9                2
NBR               -24              -                -
NBR/C5-I          -18              6               -11
NBR/C5-II         -18              6               -11
NBR/C5-C9         -18              6               -13
NBR/C9-I          -16              8               -11
NBR/C9-II         -14             10               -11
NBR/aMS           -15              9               -11

Appendix 2 - DMA results for 80/20 (wt./wt.)
polymer blends

                   TG          TG Shift
              ([degrees]C)   ([degrees]C)

EPDM              -41             -
EPDM/C5-I         -33             8
EPDM/C5-II        -33             8
EPDM/C5-C9        -36             4
EPDM/C9-I         -40             1
EPDM/C9-II        -40             1
EPDM/aMS          -41             0
NR                -62             -
NR/C5-I           -53             9
NR/C5-II          -53             9
NR/C5-C9          -51             11
NR/C9-I           -47             15
NR/C9-II          -48             14
NR/aMS            -52             10
BR                -98             -
BR/C5-I           -92             6
BR/C5-II          -88             10
BR/C5-C9          -90             9
BR/C9-I           -91             7
BR/C9-II          -92             6
BR/aMS            -87             12

                   TG          TG Shift
              ([degrees]C)   ([degrees]C)

ESBR              -52             -
ESBR/C5-I         -44             8
ESBR/C5-II        -40             12
ESBR/C5-C9        -37             15
ESBR/C9-I         -36             16
ESBR/C9-II        -37             15
ESBR/aMS          -36             16
SSBR               -7             -
SSBR/C5-I          0              7
SSBR/C5-II         1              8
SSBR/C5-C9         1              8
SSBR/C9-I          4              11
SSBR/C9-II         3              10
SSBR/aMS           4              11
NBR               -19             -
NBR/C5-I          -19             0
NBR/C5-II         -19             0
NBR/C5-C9         -17             3
NBR/C9-I          -17             3
NBR/C9-II         -14             5
NBR/aMS           -14             5


(1.) G.R. Hamed, Rubber Chem. Technol., 54, 576 (1983).

(2.) P.O. Powers', Rubber Chem. Technol., 36, 1,542 (1963).

(3.) D. W. Aubrey, Rubber Chem. Technol., 61, 448 (1988).

(4.) P. Robert et al., FR2877348 to Societe de Technologie Michelin (2004).

(5.) G. Lopitaux and D. Vasseur, FR2910906 to Societe de Technologic Michelin (2006).

(6.) M. Kralevich, et al. US6316567 to Goodyear Tire and Rubber Co. (1999).

(7.) G. Kraus and K. W. Rollmann, J. Appl. Polym. Sci., 21, 3,311 (1977).

(8.) J.B. Class and S. G. Chu, J. Appl. Polym. Sci., 30, 805 (1985).

(9.) T.G. Fox, Bull. Am. Phys. Soc., 1, 123 (1956).

(10.) VKJ. Work, K. Horie, M. Hess and R.ET. Stepto, Pure Appl. Chem., 76, 1985 (2004).

(11.) P.A.J. Small, J. Appl. Chem., 3, 71 (1953).

(12.) L.M. Robeson, Polymer Blends': A Comprehensive Review, (2007) Carl Hanser Verlag, Munich.

(13.) S. Krause, J. Macromol. Sci.- Revs. Macromol. Chem., C7, 251 (1972).

(14.) M.M. Coleman, J.E Graf and pC. Painter, Specific Interactions and the Miscibility of Polymer Blends (1991) Technomic, Lancaster.

(15.) R. Mildenberg, M. Zander, and G. Collin, Hydrocarbon Resins (1997) VCH Publishers, Inc., New York.

Laura E. Shekleton and Steven K. Henning, Cray Valley Hydrocarbon Specialty Chemicals

Table 1 - identification of hydrocarbon resins

Resin    Commercial grade (a)       Description
C5-I              Wingtack 98      Aliphatic C5
C5-II            Wingtack STS      Aliphatic C5
C5/C9                       -      C5/C9 hybrid
C9-I            Norsolene A90       Aromatic C9
C9-II           Norsolene S95       Aromatic C9
aMS            Norsolene W100      Pure monomer

(a) Cray Valley Hydrocarbon Specialty Chemicals

Table 2 - identification of elastomers

Elastomer   Commercial grade                          Description

EPDM        Nordel IP4640 (a)     Ethylene propylene diene rubber
BR            Buna CB 22 (b)             Cis-polybutadiene rubber
NR                 SMR CV-60                       Natural rubber
ESBR        Plioflex 1502 (c)   Emulsion styrene butadiene rubber
SSBR             Buna VSL VP    Solution styrene butadiene rubber
                PBR 4041 (d)
NBR         Nipol DN3335 (e)                       Nitrile rubber

(a) The Dow Chemical Company
(b,d) Lanxess Corp.
(c) The Goodyear Tire & Rubber Co.
(e) Zeon Chemicals LP.

Table 3 - hydrocarbon resin % aliphatic protons (NMR) and
glass transition temperature ([T.sub.g])

Resin   % aliphatic proton   [T.sub.g] ([degrees]C)
C5-I           96.5                    58
C5-II          91.0                    56
C5/C9          76.0                    44
C9-I           66.5                    59
C9-II          55.0                    54
aMS            48.0                    58

Table 4 - elastomer grade and glass transition temperature (Tg)

Elastomer    [T.sub.g] ([degrees]C)
EPDM                  -42
BR                   -103
NR                    -59
ESBR                  -50
SSBR                   -9
NBR                   -24

Table 5 - calculated solubility parameters ([[delta].sub.p])

         [[delta].sub.p]               [[delta].sub.p]
Resin    [(MPa).sup.0.5]   Elastomer   [(MPa).sup.0.5]

C5-I               15.75       EPDM              16.24
C5-II              15.81         NR              16.77
C5/C9              15.86         BR              16.89
C9-I               16.79       ESBR              17.03
C9-II              17.32       SSBR              16.75
aMS                17.13        NBR              19.04

Table 6 - correlation between calculated solubility parameter
differences [([DELTA][[delta].sub.p.sup.2]).sup.1/2] and the
shift in [T.sub.g] peak ([DELTA] [T.sub.g]) as measured by DMA


        [([DELTA][[deta]          [DELTA]
        .sub.p.sup.2]).sup.0.5]   [T.sub.g]

C5-I    0.49                      7.6
C5-II   0.43                      7.7
C5/C9   0.38                      4.4
C9-I    0.55                      1.1
C9-II   1.08                      0.7
aMS     0.90                      0.0
r *                    -0.74


        [([DELTA][[deta]          [DELTA]
        .sub.p.sup.2]).sup.0.5]   [T.sub.g]

C5-I    1.02                      8.7
C5-II   0.96                      8.5
C5/C9   0.91                      10.8
C9-I    0.02                      14.5
C9-II   0.55                      13.7
aMS     0.37                      9.8
r *                    -0.75


        [([DELTA][[deta]          [DELTA]
        .sub.p.sup.2]).sup.0.5]   [T.sub.g]

C5-I    1.14                      6.40
C5-II   1.08                      10.30
C5/C9   1.03                      8.50
C9-I    0.11                      7.40
C9-II   0.42                      6.40
aMS     0.24                      11.50
r *                    -0.08


        [([DELTA][[deta]          [DELTA]
        .sub.p.sup.2]).sup.0.5]   [T.sub.g]

C5-I    1.28                      7.7
C5-II   1.22                      11.7
C5/C9   1.18                      14.8
C9-I    0.25                      15.8
C9-II   0.28                      15.2
aMS     0.10                      16.0
r *                    -0.76


        [([DELTA][[deta]          [DELTA]
        .sub.p.sup.2]).sup.0.5]   [T.sub.g]

C5-I    1.00                      6.7
C5-II   0.94                      8.4
C5/C9   0.89                      7.6
C9-I    0.04                      10.9
C9-II   0.57                      10.4
aMS     0.39                      11.0
r *                    -0.57


        [([DELTA][[deta]          [DELTA]
        .sub.p.sup.2]).sup.0.5]   [T.sub.g]

C5-I    3.29                      '0.0
C5-II   3.23                      '0.1
C5/C9   3.18                      '2.7
C9-I    2.25                      2.6
C9-II   1.72                      5.2
aMS     1.90                      5.4
r *                    -0.91

* Pearson correlation coefficient
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Author:Shekleton, Laura E.; Henning, Steven K.
Publication:Rubber World
Date:Mar 1, 2013
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