An aliphatic epoxy-terminated polysulfide polymer has the formula R″—CHOH—CH2-S—R—(Sy-R)t-S—CH2-CHOH—R″ and is formed by a process, where each R is independently chosen from branched alkanediyl or branched arenediyl groups and groups with the structure —(CH2)a-O—(CH2)b-O—(CH2)c- and about 0 to about 20% of the number of R-groups are branched alkanediyl or branched arenediyl groups and about 80 to about 100% of the number of R-groups have the structure —(CH2)a-O—(CH2)b-O—(CH2)c-, where t is from about 1 to about 60, y is an average value of from about 1.0 to about 2.5, b is an integer value of from about 1 to about 8, and a and c are independently integers from about 1 to about 10, and where each R″ is independently a particular radical where, m, n, o, p, q and r independently have a value of from about 1 to about 10.